Quantum Field Theory without Infinities

Publisher： Elsevier

ISSN： 0003-4916

Source： Annals of Physics, Vol.292, Iss.2, 2001-09, pp. : 139-156

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Abstract

In relativistic quantum field theories, the traditional renormalization approach leads to Hamiltonians with infinite counterterms. The infinities cancel when this Hamiltonian is used to calculate the renormalized finite S-matrix and related observable properties in a good agreement with experiment. However, time evolution of state vectors and observables cannot be studied without a well-defined finite Hamiltonian. Based on the “clothed particle” approach (O. W. Greenberg and S. S. Schweber, 1958, Nuovo Cimento 8, 378), we reformulate the theory in such a way that ultraviolet infinities appear neither in the S-matrix nor in the Hamiltonian. In this formulation the Hamiltonian is finite and allows us to calculate the time evolution of wave functions, the S-matrix, and other properties by a straightforward application of quantum mechanical rules without renormalization. A rigorous approach to the bound states in quantum field theory is also discussed using the hydrogen atom as an example.